Neal Parker, 58, of Millville, N.J., crashed at Raceway Park in Old Bridge, state police Sgt. Stephen Jones said. He was pronounced dead at the scene.
Parker was entered in the Top Alcohol Funny Car competition. The crash occurred shortly before noon.
"Parker ... crashed Friday at a high rate of speed in the shutdown area during qualifying," the NHRA said in a statement on its website. "On behalf of everyone at NHRA and Raceway Park, we are deeply saddened and want to pass along our sincere condolences to the entire Parker family."
NHRA officials and New Jersey state police are investigating.
The car ran through a containment area with soft barriers, sand and a safety net and wound up in pieces in front of a wall at the edge of the raceway property. State police declined to comment on whether the car hit the wall or on eyewitness accounts that a drogue chute designed to slow the car failed to deploy properly.
Spectator David Farrah of Manalapan said it appeared the chute malfunctioned.
"It looked like the chute just didn't open and he couldn't stop," Farrah said. "The car was just crushed. It was tragic."
Another spectator, George Tompkins, 63, of Metuchen, said he left the stands shortly before the crash. He didn't see the wreck, but said he heard it.
"You heard that sound and knew right away that it was bad," he said.
Racing was suspended for more than three hours while the crash was being investigated.
Parker often drove in NHRA events on the East Coast, but was not among the NHRA's top-ranked drivers nationally, NHRA spokesman Anthony Vestal said.
Telephone messages left at Parker's Millville home and an excavating business listed in his name were not immediately returned Friday.
Friday's accident comes nearly two years after top racer Scott Kalitta died when his Funny Car burst into flames and crashed at the end of the track in central New Jersey.
Kalitta's Toyota Solara was traveling at about 300 mph when it burst into flames.
New Jersey State Police investigators determined that "catastrophic mechanical failure" caused the fuel-fired explosion.
The 1994 and 1995 Top Fuel season champion had 18 career victories.
In February, a spectator died after being hit by a tire from a crashing dragster at the NHRA Arizona Nationals. The woman was watching a first-round Top Fuel run when Antron Brown's Matco Tools/U.S. Army dragster went out of control on the strip and its left rear wheel came off.